4.2 Reaction Thermodynamics and Important Parameters

Cation exchange reactions

Ion exchange reactions occur when ions exchange their positions at the soid-surface – water interface. These reactions are typically assumed reversible and occur instantaneously at time scales ranging from microseconds to hours. Ion exchange is typically represented in the following form:

Here (s) and (aq) refer to solid and aqueous phases, respectively; X^- denotes the negatively charged surface sites that bound cations A^u+ and B^v+, with u and v being the charges of A and B, respectively. In this reaction, A and B are cations that compete for sorption sites (Appelo and Postma, 1993; Sposito et al., 1981; Vanselow, 1932). The equilibrium constant K_eq of reaction (1) can be expressed as

Here the parentheses [ ] represent activities. Aqueous concentrations are easily related to activities through concentration and activity coefficients. Activities of ions on solid phases are typically expressed as a fraction of the total, either as molar fraction or as equivalent fractions. The total number can be based on the number of exchange sites or as the number of exchangeable cations.

The units meq is often used in ion exchange calculations. An meq is the number of ions that sums a specific quantity of electrical charges. For example, an meq of K⁺ is about 6.02 x 10²⁰ positive charges. On the other hand, an meq of Ca²⁺ is also 6.02 x 10²⁰ positive charges, however only 3.01 x 10²⁰ ions because Ca²⁺ has two positive charges. For an ion Iⁱ⁺ with a charge of i, the equivalent fraction b_I is calculated as:

where I, J, K are exchangeable cation with charges i, j, k, respectively. A molar fraction $\beta_{I}^{M}$ is obtained by the following form:

Here TEC is the total exchangeable cations in mmol/kg sediment, not cation exchange capacity. The use of fractions should give the summation of fractions being 1, that is, ${\displaystyle \sum _{}\beta =1}$ .

Three common conventions used in writing ion exchange equilibrium constants are Gaines-Thomas convention, Gapon convention, and Vanselow convention. If the ion exchange is between cations of the same valence (homovalent exchange), the convention does not make a difference. If the exchange is between cations of different valences (heterovalent), the convention makes a difference. For example, the ion exchange reaction between Na and Ca can be written as follows:

With

Here if the equivalent fraction of the exchangeable cations is used for $β$ values, the Gaines-Thomas convention is followed (Graines and Thomas, 1953). If we use molar fractions for $β$ values, we follow the Vanselow convention (Vanselow, 1932). If the activities of cations on exchange sites are expressed as a fraction of the number of exchange sites (X-), we follow the Gapon convention, the reaction will be written as follows:

Where

Here the activities are expressed in terms of the mole fraction of the total number of exchangeable sites. To fully understand the difference between different conventions and calculation, please go over Example 6.3 in chapter 6 of Appelo and Postma (2005).

Selectivity coefficient

The capabilities of ions to compete for exchange sites are governed by their affinity to the surface of the exchangers. Selectivity coefficients have been reported in literature for common ions including Na⁺, K⁺, Ca²⁺, and Mg²⁺, however rarely for trace metals. The larger the selectivity coefficient, the higher affinity of the ion to the solid phase and the more competitive for exchange. In general, ions have high affinity to exchange sites when they have higher valence, are less solvated with water molecules, and react strongly with the surface sites. The following Table 1 lists selectivity coefficients reported in literatures for ion exchange on kaolinite (Appelo and Postma, 2005; Bundschuh and Zilberbrand, 2011).

For typical ion exchangers, the sequence of affinity is as follows: Ba²⁺> Pb²⁺ > Sr²⁺ > Ca²⁺ > Ni²⁺ > Cd²⁺ > Cu²⁺ > Co²⁺> Zn²⁺ > Mg²⁺ > Ag⁺> Cs⁺ > K⁺ >NH⁴⁺ >Na⁺ >H⁺. When there are multiple cations co-exist in the solution, the surface exchange site composition is largely determined by the cation aqueous concentration and their affinity to the exchange sites. To calculate the exchange site composition, that is, the mole fraction of each cation on the exchange site, please follow the example 6.4 in chapter 6 of Appelo and Postma (2005).

Cation exchange capacity

The cation exchange capacity (CEC, meq/kg solid) is a measure of the solid phase capacity for ion exchange reactions (Meunier, 2005). The CEC of different porous media are very much associated with their clay content, organic carbon, and grain size. Different materials have different CEC values. CEC values of clay minerals such as muscovite, illite, kaolinite, and chlorite are high for their grain sizes smaller than 2 μm (Drever, 1982). In general, organic matter has the highest CEC values (1500 - 4000 meq/kg). Iron oxides play a vital role in natural processes and controls nutrient availability and heavy-metal mobility (Houben and Kaufhold, 2011). Iron oxides, such as goethite and hematite, have CEC values from 40 to 1000 meq/kg. Many solid materials have iron oxides or organic matters coated on their surface and therefore have large CEC values. For soils, CEC value is a function of solution pH depending on hydrolysis reactions of surface sites. In general, cation exchange occurs due to the broken bonds around the crystal edges, the substitutions within the lattice, and the hydrogen of exposed surface hydroxyls that may be exchanged. Higher pH values give rise to more negative charges on clay, resulting in higher CEC. CEC values increase as the grain size decreases due to the large surface area associated with smaller grains.